Distributed continuous-time algorithm for nonsmooth optimal consensus without sharing local decision variables

A distributed continuous-time algorithm is proposed for constrained nonsmooth convex optimization. A distinct feature of our algorithm is that it does not require agents to share their local decision variables to the network, and it still achieves the optimal solution. With the help of Lagrangian functions, exact penalty techniques, differential inclusions with maximal monotone maps and saddle-point dynamics, we prove the convergence of the proposed algorithm and show that it achieves an O(1/t) convergence rate. Numerical example also illustrates the effectiveness of the proposed method. (C) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.